Position of a point relative to a circle: Examples

This lesson will cover a few examples to illustrate the concept covered in the previous lesson: position of a point with respect to a circle.

Example 1 Determine the position of the following points with respect to the given circles

(i) (3, 4) with respect to x2 + y2 – 9 = 0

(ii) (1, 0) with respect to x2 + y2 – 2x + 4y + 1 = 0

(iii) (2, 3) with respect to x2 + y2 – 6x – 4y = 0

Solution Recall that all we need to do is evaluate S1, i.e. substitute the coordinates of the given points in the corresponding circles’ equations, and check its sign. Positive means outside, negative means inside, and zero means on the circle.